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Prospects for Experimental Access to the Neutrino Mass Hierarchy Magic Baselines for Beam Neutrinos David McKee, KSU 1 December 2010 Manhattan, KS
Transcript of Prospects for Experimental Access to the Neutrino Mass ... · Prospects for Experimental Access to...
Prospects for Experimental Access
to the Neutrino Mass HierarchyMagic Baselines for Beam Neutrinos
David McKee, KSU1 December 2010
Manhattan, KS
Overview• Review of Neutrino history and physics
• Physics in Long Baseline Beam Experiments
• The “first” magic baseline
• The “short” magic baseline
• Conclusions
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Neutrino Basics & History
Invented in 1930 by Wolfgang Pauli to solve a problem with β decay spectra
First observed in 1956 by Cowan andReines using νs from a nuclear reactor:ν + p→ n+ e+.
Only interact weakly.
source: http://library.lanl.gov/cgi-bin/getfile?25-02.pdf
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Into the Cuisinart
You ought to be abe to predict the neutrinoflux from the sun (≈ 6×1014/m2/s at earthorbit), and with Cohen and Reines’ results(i.e. the cross-section) you can design acounting experiment to measure it.
Raymond Davis Jr., Kenneth C. Hoffmanand Don S. Harmer build a big tankin the Homestake mine and perform anexperimental tour de force to measure itfrom 1970 to 1994.
It came up persistently up short ofexpectation. Very short.
Some are disappearing along the way. Where are they going??
source: http://www.sns.ias.edu/
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Mixing
Neutrinos are produced in conjunction with charged leptons.
Assume a set of lepton-flavor quantum numbers.
In that case Homestake only detects νe’s (and not νµ’s or ντ ’s).
What if they are changing flavor in flight?∗
This is only possible if the mass is non-zero. But mass is assumed
to be zero. Therefore:
Physics beyond the standard model!
(*) Suggested by Gribov and Pontecorvo in 1968
jnb/Papers/Popular/Scientificamerican69/scientificamerican69.html
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Formalism for Mixing
Three flavors: e, µ, τ
Eigenstates of the weak interaction
Three masses: m1, m2, m3
Eigenstates of the free Hamiltonian
νανβ
P (να → νβ) = |〈νβ| να(t)〉|2 =∣∣⟨νβ ∣∣Ue−iEtU∗∣∣ να⟩∣∣2
=
∣∣∣∣∣∣∑i
∑j
U∗α,iUβ,j sin 2Xi,j 〈νβ| να〉
∣∣∣∣∣∣2
=
∣∣∣∣∣∣∑j>i
<[Uα,iU
∗β,iU
∗α,jUβ,j
]sin2Xi,j +
∑j>i
=[Uα,iU
∗β,iU
∗α,jUβ,j
]sin 2Xi,j
∣∣∣∣∣∣2
where U is a unitary mixing matrix and Xi,j =m2
i−m2j
4EL.
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More Formalism
U =
1 0 00 c23 s230 −s23 c23
c13 0 s13e
−iδCP0 1
−s13eiδCP 0 c13
c12 s12 0−s12 c12 0
0 0 1
where cij = cos (θij) andsij = sin (θij)
Free Parameters
Three mixing angles: θ12, θ23, θ13
A CP violating phase: δCP(Two Majorana phases not shown: η1, η2)
Every term in the probability has at least four trig(θij)s in it!
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Knowns and Unknows
quantity value notes
sin2 (2θ12) 0.87±0.03 KamLAND, solar, SNO, ...
sin2 (2θ23) > 0.92 SuperK, MINOS...
sin2 (2θ13) < 0.2 at 90% C.L. from Chooz
∆m221 7.6(2)× 10−5 eV KamLAND, solar, SNO ...
|∆m232| or |∆m2
31| 2.43(13)× 10−3 eV MINOS, atmospheric, K2K ...
δCP Unknown
All θi,j ∈ [0, π2] and δCP ∈ [0,2π]. Note that sin2 (2θ13) and
∆m221/∆m2
31 are “small”.
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Matter Effect
All of the above assumes the neutrino propagating in free space,
but if the neutrino travels in matter the neutrinos can interact.
e, p, n
Z(Q2 = 0)
νν
νee
W±(Q2 = 0)
eνe
Hard scattering that removes the neutrinos from the beam are
rare owning to the very small cross-section, but coherent forward
scattering contributes and is different for electron neutrinos...
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Matter Effect
Modification of the terms
The total effect of the coherent forward scattering is to add an
effective potential V =√
2GFne where ne is the electron density.
The Hamlitonian there for looks like
1
2E
U m2
1 0 00 m2
2 00 0 m2
3
U∗+
A 0 00 0 00 0 0
where A = 2V E.
We write ∆m221 = α∆m2
31 and expand in terms of α.
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Matter Effect
Simplification
That expansion lets you write the Hamiltonia as
∆m231
2EU23
U13U12
0 0 00 α 00 0 1
U∗12U∗13 +
A
∆m231
0 0
0 0 00 0 0
U∗23
where the Uijs are the sector by sector mixing matrices exhibited
previously, and greatly reduces the number of terms to be
retained.∗
∗Freund, Phys. Rev. D 64 053003 (2001)
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Understanding long baseline physics
Consider a long baseline experiment either P (νe → νµ) orP (νµ → νe) with matter or anti-neutrinos.
Peµ ≈ sin2 2θ13 sin2 2θ23sin2[(1− A)∆]
(1− A)2
±α sin2 2θ13ξ sin δCP sin ∆sin(A∆)
A
sin[(1− A)∆]
(1− A)
+ α sin2 2θ13ξ cos δCP cos ∆sin(A∆)
A
sin[(1− A)∆]
(1− A)
+ α2 cos2 2θ23 sin2 2θ12sin2(A∆)
A2(1)
where ξ = cos θ13 sin 2θ12 sin 2θ23, A = ±(2√
2GFneE)/∆m231,
and ∆ = ∆m231L/(4E)
Positive(negative) for νe → νµ (νµ → νe)
Same as (opposite of) ∆m231 for neutrinos (anti-neutrinos)
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The “first” magic baseline
If sin(A∆) vanishes then equation 1 simplifies to
Peµ ≈ sin2 2θ13 sin2 2θ23sin2[(1− A)∆]
(1− A)2
So set
A∆ = 2√
2GFneL/(4) = 2π
and solve for L in terms of an assumed constant value of ne. You
get 7630 km (or about 7250 if you use a numeric integration and
a model Earth)
A long way!
Huber and Winter, Phys. Rev. D 68 (2003)
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A Shorter Magic Baseline
Choose L and E such that sin[(1− A)∆
]cancels for the inverted
hierarchy and is near maximal for the normal hierarchy.
(1− A)∆ =
(1∓
2√
2GFneE
δm231
)∆m2
13L
4E
=∆m2
31L
4E∓√
2
2GFneL =
π Inverted hierarchy
π/2 Normal hierarchy
Solved this gives L = 2540 km and E = 3.3 GeV.
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Expectations at the Short Magic Baseline
arXiv 0908:3741v3
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Hey, Look!
In terms of detector rate, 2500 km is a lot more manageable
than 7500 km and it so happens that we have a plausible
accelerator/detector site pair...
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Sensitivity
Exposure (kton-years)sin2 2θ13 Normal Inverted
0.10 0.022 0.0480.08 0.026 0.0680.06 0.051 0.1050.04 0.104 0.1950.02 0.425 2.600
The table shows the estimated exposureneeded to make a 3σ determination ofthe mass hierarchy as a function of thetrue value of θ13 and assuming a 1023
POT per year at 2540 km and assumingneutrino only running.
Because the beam is not mono-energetic there is sensitivity to δCP .The figure shows expected error barsaround 15 pairs of (θ13, δCP) includingsystematics for 5 years neutrinos and5 years anti-neutrinos assume a normalhierarchy.
-180
-120
-60
0
60
120
180
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
δ cp
sin2 2θ13
ν + ν _
, NH
2540km +NOνA + T2K+ DayaBay
true pts 1σ 2σ
x
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Conclusion
• Magic baselines reduce the ambiguity implicit in 3-flavor
oscillation (especially with the matter effect)
• The first (long) magic baseline is another handle on θ13
independent of energy and CP violating effects. There is
the potential for high precision than from existing reactor
experiments. But sill suffer from low far detector rates for
the foreseeable future.
• The “short” magic baseline is more practical and is primarily
sensitive to the mass hierarchy.
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